A cloud data center may provide cloud computing services to various computing systems such as desktops, laptops, tablets, smartphones, embedded computers, point-of-sale terminals, and so on. A cloud data center may have many thousands of servers and storage devices and provide various software products such as operating systems, databases, and applications. Rather than maintaining their own data centers, many enterprises subscribe as customers of a database service of a cloud data center to store and process their data. For example, a retail company may subscribe to a database service to store records of the sales transactions at the company's stores and use an interface provided by the database service to run queries to help in analyzing the sales data. As another example, a utility company may subscribe to a database service for storing meter readings collected from the meters of its customers. As another example, a governmental entity may subscribe to a database service for storing and analyzing tax return data of millions of taxpayers.
Enterprises that subscribe to such cloud-based database services want to ensure the privacy of their data. Although cloud data centers employ many sophisticated techniques to help preserve the privacy of customer data, parties seeking to steal such customer data are continually devising new counter-techniques to access the data. To help ensure the privacy of their data, many customers may encrypt their data locally before sending their data for storage by a database service. For example, each point-of-sale terminal of a retail company may encrypt the sale amount of each transaction and send the sale amount only in an encrypted form to the database service as a record of the transaction. If the retail company wants to determine the total sale amount for each store, the encrypted sale amounts for each store would need to be downloaded to a company computer and then decrypted. The decrypted sale amounts for each store could then be added together to generate the total sale amount for each store.
If a customer were to use a homomorphic encryption of data, then the downloading and decrypting of all the sales data could be avoided. Homomorphic encryption has the characteristic that a computation performed on the encrypted data generates an encrypted result that, when decrypted, equals the same result as if the computation was performed on the unencrypted data. For example, if the retail company homomorphically encrypts its sale amounts, then the database service could add the encrypted sale amounts for each store to generate an encrypted total sale amount for each store. The retail company need only download the encrypted total sale amount for each store and decrypt those total sale amounts.
Although homomorphic encryption allows the aggregation of encrypted data to be performed by the database service and thus avoids the downloading of the unaggregated encrypted data, homomorphic encryption can be very computationally expensive. Homomorphic encryption schemes typically use complex mathematical operations such as multiplications, exponentiations, matrix operations, and so on. As a result, many organizations either choose not to use homomorphic encryption or need to expend significant amounts of money purchasing additional computational power that is needed to support homomorphic encryption.